Tool to list the possible positions of a cube. A die is a cube with 6 differentiated faces, it can be defined by its visible faces so as to know its possible orientations / rotations.
Cube Rotation - dCode
Tag(s) : Fun/Miscellaneous
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!
Place the cube on one side and orient it according to the 4 directions. Move to the next position (other side) and so on to get all rotations.
The die can fall on one of the 6 faces possible and be oriented according to 4 angles, or 24 possibilities. $$ 6 \times 4 = 24 $$
There are 4 types of rotation of a dice:
- Rotation according to the diagonals
- Rotation along the axis connecting the centers of 2 opposite faces
- Rotation along the axis connecting the centers of 2 opposite edges
- Identity rotation (original stationary state)
A cube whose faces are undifferentiated with 13 axes of symmetries:
- 3 axes pass through the centers of the faces, a cube has 6 faces, so 3 axes
- 6 axes pass through the centers of the opposite edges, a cube has 12 edges, so 6 axes
- 4 axes go through the opposite corners, a cube has 8 angles, so 4 axes